Chapter 14: Cost minimization

Question 1

Comparative statics analysis of changes in input prices

Answer 1

When the firm has smooth isoquants with a diminishing TRS, and is initially
using positive quantities of an input, an increase in the price of that input
(holding output and other input prices fixed) will cause the cost-minimizing
quantity of that input to go down.

Question 2

An expansion path

Answer 2

An expansion path is a line that connects the cost-minimizing input
combinations as the quantity of output varies, holding input prices constant.

Question 3

A normal input

Answer 3

A normal input is an input whose cost-minimizing quantity increases as the
firm produces more output.

Question 4

An inferior input

Answer 4

An inferior input is an input whose cost-minimizing quantity decreases as the
firm produces more output.

Question 5

Shephard’s Lemma

Answer 5

Shephard’s Lemma tells us that if we know the cost function, we can derive
the input demand functions.

Question 6

The short-run cost function

Answer 6

The short-run cost function is defined as the minimum cost to produce a
given level of output, only adjusting the variable factors of production.

Question 7

The long-run cost function

Answer 7

The long-run cost function gives the minimum cost of producing a given level
of output, adjusting all of the factors of production.

Question 8

An isocost line

Answer 8

is the set of combinations of inputs that yield the same total cost for the firm:

Question 9

The cost minimization problem

Answer 9

find the point on the isoquant that has the lowest possible isocost line associated with it.

Question 10

conditional factor demands

Answer 10

The optimal choices of inputs x1(w1, w2, y) and x2(w1, w2, y) are called the
conditional factor demands or derived factor demands.

Conditional factor demands give the cost-minimizing choices for a given level of
output while profit maximizing factor demands give the profit-maximizing
choices for a given price of output.

Question 11

A (total) cost function

Answer 11

is a mathematical relationship that shows how total costs of a cost-minimizing firm vary with the quantity of output and the prices
of inputs.

This function is also called the long-term cost function because it gives you the total costs after all inputs have been optimally chosen.